NONLINEAR MANIFOLD REPRESENTATIONS FOR FUNCTIONAL DATA

作者：Chen Dong^*; Mueller Hans Georg

来源：Annals of Statistics, 2012, 40(1): 1-29.

DOI：10.1214/11-AOS936

• Functional data analysis
• modes of functional variation
• functional manifold components
• dimension reduction
• smoothing

For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which we modify to address functional data settings. In simulations and applications, we study examples of functional data which lie on a manifold and validate the superior behavior of manifold mean and functional manifold components over traditional cross-sectional mean and functional principal components. We also include consistency proofs for our estimators under certain assumptions.

• 出版日期2012-2